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Answer to Question #25248 in Abstract Algebra for Mohammad

Question #25248
Show that the following are equivalent:
(A) If I is a nil ideal in any ring R, then Mn(I) is nil for any n.
(B)' If I is a nil ideal in any ring, then M2(I) is nil.
Expert's answer
That (A) implies (B) is obvious,since it is case n=2.For, if (B) holds, then for any nilideal I, m=2t , Mm (I) is isomorphic to M2(Mm/2(I)) is also nil, by induction on t. Since any n is bounded by 2t forsome t, we have (A).

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